Trigonometric Equations Question 131
Question: The angle of elevation of the top of the tower observed from each of the three points $ A,B,C $ on the ground, forming a triangle is the same angle $ \alpha $ . If R is the circum-radius of the triangle ABC, then the height of the tower is
[EAMCET 1994]
Options:
A) $ R\sin \alpha $
B) $ R\cos \alpha $
C) $ R\cot \alpha $
D) $ R\tan \alpha $
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Answer:
Correct Answer: D
Solution:
- Since the tower makes equal angles at the vertices of the triangle, therefore foot of the tower is at the circumcentre. From $ \Delta OAP, $ we have $ \tan \alpha =\frac{OP}{OA} $
$ \Rightarrow $ $ OP=OA\tan \alpha $
$ \Rightarrow $ $ OP=R\tan \alpha $ .
BETA
